The invention relates to a method and to an arrangement for the representation of a halftone image wherein the halftone image is formed of different intensity stages produced by use of picture elements of identical size situated at prescribed grid positions of a two-dimensional grid. A respective prescribed plurality of grid positions of the grid are combined to form an image spot. The number of picture elements and their grid positions within the image spot define the respective intensity stage or step.
Many reproduction devices employed in electronic data processing relate to digital displays. Their individual reproduction elements can assume two states, for example on-off, bright-dark, or reflective-absorbing. Such devices are: AC plasma screens, LCD displays, dot-matrix printers, etc. Digital displays are particularly suited for the reproduction of drawings and alpha-numeric characters. It is more difficult to reproduce halftone images since all reproduction elements have the same size. One possibility for reproducing halftones is the variation of the arrangement and plurality of elements in the two states. Generating this type of brightness gradation is referred to as the pseudo-halftone method.
Such a pseudo-halftone method for the representation of a halftone image is disclosed, for example, in U.S. Pat. No. 4,374,388, incorporated herein by reference.
In the pseudo-halftone method, a decision about its state must be undertaken for every reproduction element. This occurs by a comparison between the intensity of the picture element to be reproduced and a threshold va1ue. When the intensity is greater than the threshold value the reproduction element assumes the bright state, otherwise it assumes the dark state. Dependent upon how the threshold value is defined, one distinguishes between adaptive and non-adaptive algorithms.
Given non-adaptive algorithms, the threshold value of a reproduction element is fixed as a function of its position and is independent of the image to be reproduced or of the already decided states of other reproduction elements. The threshold values of a plurality of reproduction elements can be combined to form a matrix which, periodically repeating, covers the entire character area. Grids known to have non-adaptive algorithms are: ordered Dither raster, single thresholding, digital halftone, and stochastic grids.
Adaptive methods employ a plurality of picture elements and bright-dark decisions which have already been made in order to identify the threshold values. Methods of this type are constrained average, overflow counting, error diffusion, and dynamic thresholding.
Adaptive algorithms require a significantly greater hardware expense because the intensity values of the picture elements and the decisions undertaken must be available in the environment of the reproduction element now under consideration. The identification of the threshold values from these data in turn involves a considerable processing and time expense. The non-adaptive algorithms are thus faster, and parallel operation (simultaneous processing of a plurality of lines) is possible. Fundamentally, simple hardware circuits thus suffice in order to execute the comparison between the brightness to be reproduced and the threshold.
When reproductions based on adaptive and non-adaptive algorithms are compared, then some significant differences between them can be identified. Because the prior history enters into the determination of the thresholds, given adaptive algorithms, the same detail is reproduced better in the one instance and poorer in another instance, dependent on the environment. The observer is more inclined to disregard regular textures. These, however, are generally not formed given adaptive algorithms, but rather change. It is disturbingly noticeable in color reproduction that the color separations do not coincide everywhere. Thus, color points which are intended to produce a mixed color together sometimes fall on top of one another, and sometimes fall side-by-side. A reproduction with adaptive and non-adaptive algorithms is equivalent only when the individual color points are not perceived, i.e. when the texture is below the threshold, insofar as the subtractive color mixing on the paper in fact occurs linearly. When, however, the texture reaches the threshold or crosses it, an additional restlessness arises which produces a grainy, rough impression in the reproduction or copy even in uniform regions in the original. On the other hand, given adaptive algorithms, the fluctuations from the brightness to be reproduced which are produced due to the digitization are smaller in a tight space and the edge steepness at bright-dark transitions can be regulated.
When a reproduction with an adaptive algorithm is viewed from a distance from which the texture lies above the perceptability threshold, there are individual regions which are particularly beautiful. Although the texture is clearly perceived, it has roughly the same wavelength and intensity at these locations for different intensity values and the superimposition of colors does not form any Moire patterns.
The concept of privileged direction has far-reaching significance in the discrimination of grids having reproduction elements which are of the same size and are uniform. Privileged directions are those directions in which neighboring reproduction elements which are equidistant from one another are situated.
The question regarding the possible number of privileged directions can be reduced to the question of which regular polygons completely cover the plane. From the geometry it is known that only the equilateral triangle, the square, and the regular hexagon meet this condition. The square has four equidistant neighbors so that two privileged directions perpendicular to one another result. Triangle and hexagon are equivalent with respect to the privileged direction because the hexagon is constructed of equilateral triangles. Three privileged directions result from the six neighbors, these describing an angle of 120.degree. with one another as is disclosed in greater detail, for example, in German Pat. No. 29 43 018, incorporated herein by reference.
Grids having two privileged directions are also referred to as square grids, and those having three privileged directions are referred to as hexagonal grids.
More than three privileged directions are not possible due to the arrangement of the reproduction elements. For generating intensity gradations given non-adaptive algorithms, a plurality of reproduction elements are combined to form a continuously repeating structure covering the character field, i.e. the image spot. If the directions of neighboring image spots are included in the definition of privileged directions, then 2, 4, or 6 privileged directions can occur given square grids, and 3, 4, 5, or 6 privileged directions can occur given hexagonal grids. The possibility of creating more than two or three privileged directions does not exist given the grids with variable point size which are currently almost exclusively employed in printing technology. Only in color printing can the grids for the individual inks be rotated relative to one another in order to create new privileged directions.
The quality of a reproduction becomes all the better the smaller the reproduction elements are selected. Simultaneously, however, the hardware expense and the time required for the reproduction increase. In addition, physical boundaries are encountered depending on the method, these causing a minimum size of the reproduction elements. A grid which would lead to an improvement of the reproduction quality by a few 10% given the same size of the reproduction elements would thus have considerable advantages. A number of demands are to be made of a grid with which images are to be generated according to the pseudo-halftone method. It should be in a position to reproduce fine details. The size of the reproduction elements thereby defines the absolute limits. Differing results, however, are obtainable within this framework on the basis of the arrangement of the reproduction elements and the distribution of the thresholds within the image spot.
Closely connected with the detail reproduction is the capability of sharply reproducing black-white transitions, and of avoiding frazzle. The edge sharpness is of significance, particularly given lines and lettering, because two transitions lie in tight proximity therein.
The digitization causes two further disruptions related to one another. These disruptions relate to structures not present in the original but which occur in the reproduction. First, moire patterns are to be noted. They can arise when the frequency of a regular original arrives in the range of the frequency of the reproduction elements.
Second, generating halftones by variation of the number of reproduction elements in the two states causes the formation of textures within regions of constant intensity. The uniform impression of such a region thus only arises in the eye of the observer when it is no longer capable of perceiving the individual elements of the texture. Immediately following therefrom is that the nature of this texture has a considerable influence on the reproduction quality of a grid, particularly since it likewise influences the afore-mentioned evaluation criteria. A measured quantity or value for the ability to perceive textures within the gray scales of a gray key (gray scale) is as follows: the distances from which the gray scales appear uniform and even to the observer, and the textures dissolve. These distances are therefore referred to below as dissolve distances.